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Netlab Reference Manual linemin
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<H1> linemin
</H1>
<h2>
Purpose
</h2>
One dimensional minimization.

<p><h2>
Description
</h2>
<CODE>[x, options] = linemin(f, pt, dir, fpt, options)</CODE> uses Brent's
algorithm to find the minimum of the function <CODE>f(x)</CODE> along the
line <CODE>dir</CODE> through the point <CODE>pt</CODE>.  The function value at the
starting point is <CODE>fpt</CODE>.  The point at which <CODE>f</CODE> has a local minimum
is returned as <CODE>x</CODE>.  The function value at that point is returned
in <CODE>options(8)</CODE>.

<p><CODE>linemin(f, pt, dir, fpt, options, p1, p2, ...)</CODE> allows 
additional arguments to be passed to <CODE>f()</CODE>.

<p>The optional parameters have the following interpretations.

<p><CODE>options(1)</CODE> is set to 1 to display error values.

<p><CODE>options(2)</CODE> is a measure of the absolute precision required for the value
of <CODE>x</CODE> at the solution.

<p><CODE>options(3)</CODE> is a measure of the precision required of the objective
function at the solution.  Both this and the previous condition must be
satisfied for termination.

<p><CODE>options(14)</CODE> is the maximum number of iterations; default 100.

<p><h2>
Examples
</h2>
An example of the use of this function to find the minimum of a function
<CODE>f</CODE> in the direction <CODE>sd</CODE> can be found in <CODE>conjgrad</CODE>
<PRE>

x = linemin(f, xold, sd, fold, lineoptions);
</PRE>


<p><h2>
Algorithm
</h2>

Brent's algorithm uses a mixture of quadratic interpolation and golden
section search to find the minimum of a function of a single variable once
it has been bracketed (which is done with <CODE>minbrack</CODE>).  This is adapted
to minimize a function along a line.
This implementation
is based on that in Numerical Recipes.

<p><h2>
See Also
</h2>
<CODE><a href="conjgrad.htm">conjgrad</a></CODE>, <CODE><a href="minbrack.htm">minbrack</a></CODE>, <CODE><a href="quasinew.htm">quasinew</a></CODE><hr>
<b>Pages:</b>
<a href="index.htm">Index</a>
<hr>
<p>Copyright (c) Ian T Nabney (1996-9)


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